A208226 a(n)=(a(n-1)*a(n-3)^4+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

1, 1, 1, 1, 2, 3, 5, 83, 3364, 700861, 6652337263549, 10264082055393717193904815, 736193034562641516492404723890409674438627151, 2057106833431631102316572923185391939849261245309254135929044995902093016346478213863681606

Offset: 0

Author

Matthew C. Russell, Apr 25 2012

Keywords

• nonn

Comments

This is the case a=4, b=1, c=1, y(0)=y(1)=y(2)=y(3)=1 of the recurrence shown in the Example 3.3 of "The Laurent phenomenon" (see Link lines, p. 10).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..16
• Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

Crossrefs

Cf. A048736, A208223, A208227.

Programs

Maple

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)*y(n-3)^4+y(n-2))/y(n-4): end:
seq(y(n),n=0..13);

Mathematica

a[n_]:=If[n<4,1, (a[n - 1] *a[n- 3]^4 + a[n - 2])/a[n - 4]]; Table[a[n], {n, 0, 12}] (* Indranil Ghosh, Mar 19 2017 *)
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]a[n-3]^4+ a[n-2])/ a[n-4]},a,{n,14}] (* Harvey P. Dale, Dec 29 2018 *)

Extensions

One more term from Harvey P. Dale, Dec 29 2018